Boolean algebra

Turn a Boolean statement into its truth table, canonical forms and a minimal sum of products. The finished working exports as $\LaTeX$ .

p 2 minterms · 1 term after minimising

Minterms and maxterms

Σm = 2, 3

ΠM = 0, 1

Minimal sum of products

Canonical SOP

p ∧ ¬q ∨ p ∧ q

Canonical POS

(p ∨ q) ∧ (p ∨ ¬q)

Prime implicants

p covers 2, 3 essential

Reading the result

The truth table lists every assignment of the variables. Minterms are the rows where the statement is true; maxterms are the rows where it is false. The canonical forms spell those rows out fully.

The simplifier uses the Quine–McCluskey method. It combines adjacent minterms into prime implicants, then chooses essential prime implicants and a small cover for the rest. The result is a minimal sum of products, not merely a different-looking equivalent statement.

Syntax

Negation: ~p or !p.
Conjunction: p & q.
Disjunction: p | q or p v q.
Exclusive or: p ^ q.
Implication: p -> q.
Equivalence: p <-> q.
Constants: 0 and 1.

Export

The $\LaTeX$ tab previews the document and lets you copy or download the .tex source. The export includes the truth table, canonical forms, prime implicants and the minimised expression.